LSSVM-Monte Carlo定价高维美式期权

Pricing high-dimension American option by LSSVM-Monte Carlo

随着美式期权维数的增加,存在所谓的“维数灾难”问题,为了克服这一难题,最小二乘支持向量机(LSSVM)被应用于定价高维美式期权.首先用M-C方法仿真美式期权标的物的多条价格路径,接着采用最小二乘支持向量机作为求条件期望的回归算子,并提出了一种基于改进序列优化(ISMO)的LSSVM的训练算法.针对4种不同的美式期权支付函数,给出了该方法应用于标的资产的个数分别为5和30的算例.研究结果表明,所提出的方法能很好地解决高维美式期权定价问题.

Least-squares SVM（LSSVM） was applied to pricing high-dimension American option to solve the so-called ＂dimension curse＂ problem along with the rise of dimension. Firstly, Monte Carlo（M-C） method was used to simulate many price paths of underlying assets, and LSSVM worked as regress operator for solving the conditional expectation. Moreover, training algorithm of LSSVM was proposed based on improved sequential minimal optimization （ISMO） method. Aiming at four various payment functions, an example was given when the numbers of underlying assets were respectively 5 and 30. Results show that the method proposed can solve high-dimension American option pricing problem well.